Hanoi, January 28th 2015

Quang DinhDEIB – Politecnico di Milano

IMRR Project

7 – Emulators of the Delta model

INTEGRATED AND SUSTAINABLE WATER MANAGEMENT OF RED-THAI BINH RIVER SYSTEM

IN A CHANGING CLIMATE

IMRR phases

econnaissance

odeling the system

ndicators identification

cenarios definition

lternative design

valuation

RMISAE

omparisonC

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Delta model 320 Rivers & canals with 4200 km ~ 8000 Cross sections 29 Bridges 148 Drainage culverts 89 Sluice gates 160 Pumping stations from main river 303 Pumping stations from 11 irrigation

districts

complete description of the system at each time step

~ 2 days for 16 years simulation

MIKE11

More than 16000 state varia

bles!

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• point to point information is required

• ~ 350 million years simulation for 1 policy

The model simulation must be extremely fast (1 yr in few milliseconds)

In the IMRR Project

Lumped model, computationally

efficient

Emulators

MIKE11

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Emulators

Reference: S. Galelli and A.Castelletti (2013), Tree-based iterative input variable selection for hydrological modeling, Water Resources Research, 49(7), 4295-4310.

Select among the PB model (Delta model) output components, one component y, the dynamic of which we like to emulate

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JS

JH JF

EmulatorsStep 0: Output selection

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JS

JH JF

htHN – mực nước ngày tại Hà Nội

EmulatorsStep 0: Output selection

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JS

JH JF

dt: tổng lượng nước thiếu vùng đồng bằng trong ngày t

EmulatorsStep 0: Output selection

EmulatorsStep 0: Output selection

Evaluation of other indicators• qST: daily flow at Son Tay control station (for the

environmental indicators)

• hPL & hTQ: daily water level in Pha Lai & Tuyen Quang (for the flood indicators)

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Choose: hHN, d, qST, hPL & hTQ

Emulators

Prepare a sample data set

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htHN

Dt

qtST

htTQ

htPL

rHB, rTB, rTQ

qHY , qYB

minor & lat. flows

tt

wt

Vt

dt

EmulatorsStep 1: Sample dataset

t, t-1,t-2,…

• Dataset plays a critical role in building the emulator

• constituted by N tuples {inputs, output}

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10. Các sự kiện thủ văn cực đoanTomorrow 9:00-10:00

EmulatorsStep 1: Sample dataset

List of experiments:

• Exp1: 17 yrs (Oct,1994-Oct, 2010), using historical flows

• Exp2: 17 yrs (Oct,1994-Oct, 2010), using natural flows (the case in which

reservoirs were not presented)

• Exp3: 2 yrs in which big flood occurred (1969 & 1971)

• Exp4: 1969, 1971, 1996 with 300 & 500 yrs return periods

• Exp5: 10 yrs, corresponding to 10 extreme yrs (5 floods + 5 droughts)

• Exp6: 10 yrs with 100, 200, 300 & 500 yrs return period

More than 22,630 tu

ples!

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EmulatorsStep 1: Sample dataset

List of experiments:

• Exp1: 17 yrs (Oct,1994-Oct, 2010), using historical flows

• Exp2: 17 yrs (Oct,1994-Oct, 2010), using natural flows (the case in which

reservoirs were not presented)

• Exp3: 2 yrs in which big flood occurred (1969 & 1971)

• Exp4: 1969, 1971, 1996 with 300 & 500 yrs return periods

• Exp5: 10 yrs, corresponding to 10 extreme yrs (5 floods + 5 droughts)

• Exp6: 10 yrs with 100, 200, 300 & 500 yrs return period

Data set was splitted in two sub-sets: trainings & validation (cross-validation)

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Emulators

•model is identified (but extra-tree)

adopt ANN to emulate this model to, later on, embed it into MO optimization framework

•The input that are most relevant in explaining I-O behavior of the PB model, with respect to y, are recursively selected, until all the selected state variables are given a dynamic description

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ANN: Artificial Neural Network

Emulators in

puts

neurons

output

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EmulatorsHow to choose the number n of its neurons?

• n too low reduces the accuracy, but the ANN computation is faster

• n too high: opposite

the identification was repeated for different values of n

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Emulators Step 2-4: Iterative Input variable Selection & Emulator Building

• Water level at Ha Noi

• Total supply deficit

• Flow at Son Tay

• Water level at Tuyen

Quang & Pha Lai

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Emulators Step 2-4: IIS & EB – Water level at Ha Noi

Order Variable ΔR2 R2

1 QtD 0.98521 0.98521

2 htHN 0.0105 0.99571

3 tt 0.00002 0.99573

• htHN: the daily mean water level at Ha Noi section between [t-1,t)

• tt: daily maximum tide at river mouth

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5 neurons 1 output

wlt+1HN

3 inputs

QtD

htHN

tt

Emulators Step 2-4: IIS & EB – Water level at Ha Noi

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Emulators Step 2-4: IIS & EB – Water level at Ha Noi

Statistic Monolithic emulator

R2 0.9923

mean err [%] 4.2707

st. dev. err [%] 8.7666

max err [m] 2.4752

min err [m] -2.0242

max(err99) [m] 1.6474

μ(|err99|) [m] 0.3658

min(err47) [m] -1.4580

μ(|err47|) [m] 0.0996

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Emulators Step 2-4: IIS & EB – Water level at Ha Noi

• dry season: interested in the effects of low water levels

• flood season: interested in the effects of the high water levels

would it not be better to consider specialized emulators in the different seasons?

• Build a cluster of 3 different emulators:

- dry season (15/11 - 15/5)

- flood season (1/7 – 15/9)

- two intermediate seasons

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Emulators Step 2-4: IIS & EB – Water level at Ha Noi

• dry season: 7 neurons

• flood & intermediate seasons: 5 neurons

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Emulators Step 2-4: IIS & EB – Water level at Ha Noi

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Dynamic emulator:

Quy hoạch động ngẫu nhiênStochastic Dynamic Programming (SDP)

Giải thuật di truyền Genetic Algorithm (GA)

Emulators Step 2-4: IIS & EB – Water level at Ha Noi

Non-dynamic emulator: by excluding water level at Hanoi

• we identified an ANN emulator with 5 neurons

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Dynamic emulator:

Emulators Step 2-4: IIS & EB – Water level at Ha Noi

Dynamic

Non-dynamic

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Emulators Step 2-4: IIS & EB – Water level at Ha Noi

Dynamic

Non-dynamic

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Emulators Step 2-4: Iterative Input variable Selection & Emulator Building

• Water level at Ha Noi

• Total supply deficit

• Flow at Son Tay

• Water level at Tuyen

Quang & Pha Lai

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Emulators Step 2-4: IIS & EB – Total supply deficit

Order Variable ΔR2 R2

1 wt 0.6983 0.6983

2 Vt0.1377 0.8360

3 QtD 0.0494 0.8854

4 tt0.0049 0.8903

! Canals system behaves like a reservoir:

•store water when it can be withdrawn from the river

•supply it to the fields when the water demand requires it.

• We identified an ANN emulator with 5 neurons

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Emulators Step 2-4: IIS & EB – Total supply deficit

Order Variable ΔR2 R2

1 Vt 0.9850 0.9850

2 tt0.0030 0.9880

3 wt0.0021 0.9901

4 QtD 0.0023 0.9924

• we identified an ANN emulator with 5 neurons

• Vt would not be known without the Delta model identify one more emulator to evaluate it

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Emulators Step 2-4: IIS & EB – Total supply deficit

Delta model

Emulator

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Emulators Step 2-4: IIS & EB – Total supply deficit

Delta model

Emulator

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Emulators Step 2-4: IIS & EB – Total supply deficit

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Emulators Step 2-4: IIS & EB – Total supply deficit

Order Variable ΔR2 R2

1 wt 0.7752 0.7752

2 QtD 0.1218 0.8970

3 tt0.0308 0.9278

• we identified an ANN emulator with 5 neurons

Non-dynamic V emulator: by removing the water volume V stored in the canals from the possible inputs

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Emulators Step 2-4: IIS & EB – Total supply deficit

Non-dynamic V emulator

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Emulators Step 2-4: Iterative Input variable Selection & Emulator Building

• Water level at Ha Noi

• Total supply deficit

• Flow at Son Tay

• Water level at Tuyen

Quang & Pha Lai

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

•network has to be dynamic & we consider qST among inputs

•• tide & water demand are not relevant in Son Tay

•sum QD of the upstream flows (releases + unregulated flows)

can be used instead of using each single output

•Delay time is generally lower than 1 day considered 2 cases

1 day delay

no delay

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

• we identified an ANN emulator with 5 neurons

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

1971

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

1996

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

• qST is used to evaluate the environmental indicators

the emulator has to fit well especially for low flows

•training & validation dataset only flows below 5400 m3/s (75th

quantile of the historical time series of flows at ST)

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

• All have high performances in term of R2

• the last one gives better fitting (also considering errors on the

extremes)

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

1997

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Emulators Step 2-4: IIS & EB – Flow at Son Tay

2003

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Emulators Step 2-4: Iterative Input variable Selection & Emulator Building

• Water level at Ha Noi

• Total supply deficit

• Flow at Son Tay

• Water level at Tuyen

Quang & Pha Lai

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Thanks for your attention

XIN CẢM ƠN

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